Economics 421 - Econometrics

Syllabus for Winter 2009

Quick Links: Lectures, Homework, Past Midterms, Past Finals, Video Playlist

Introduction to Econometrics
Course: Economics 421/521
Professor: Mark Thoma
Office/Hours: PLC 471 on M/W 3:30-4:30 p.m.
Phone/Email: (541) 346-4673, mthoma@uoregon.edu
Web Page: http://economistsview.typepad.com/economics421/

Course Description: This course is a continuation of the econometrics sequence. The first course, EC 420/520, introduces the linear regression model and discusses estimation and testing under (mostly) ideal conditions. This course looks at what happens when the conditions are less than ideal due to departures from the assumptions necessary for ordinary least squares to be the best linear unbiased estimator, and then provides alternative regression techniques that address  problems arising from the violations of the basic assumptions.

Text: Dougherty, Christopher, Introduction to Econometrics, 3rd ed. (Oxford: University Press, 2007)

Prerequisites: Economics 420 or the equivalent.

GTFs, Office Hours, Location, and Email Address:

Matt Cole

Hours: W 10-11

PLC 520

mcole@uoregon.edu

Lab Times:

Lab	21820	1600-1720	Thu	442 MCK
Lab	21821	1800-1920	Thu	442 MCK

Tests and Grading: There will be a midterm exam and a final. The midterm will be given Monday, February 9th. The final will be given on Tuesday, March 17th at 3:15 p.m. No make-up exams will be given. The midterm is worth 30% and the final is worth 40%. Grades will be assigned according to your relative standing in the class.

Empirical Project: There will be an empirical paper that will comprise 15% of your grade. The paper is due no later than Wednesday, March 11 at the beginning of class. Details will be given during lecture.

Computer Labs: The statistical software package EViews will be used for estimation and testing. Labs will consist of instruction and examples helpful in completing the homework assignments, and other activities. The homework is worth 15% of your grade.

*Tentative* Course Outline:

We will cover the following chapters:
Review of Multiple Regression and Hypothesis Testing
Heteroscedasticity	Ch. 7
Autocorrelation	Ch.12
Stochastic regressors and measurement errors	Ch. 8
Simultaneous Equations Estimation	Ch. 9
And, as time permits:
Binary Choice Models and Maximum Likelihood Estimation	Ch. 10
Models Using Time Series Data	Ch. 11

More details on the readings, homework, homework due dates, etc. will be posted here on an ongoing basis, so please check back regularly.

YouTube Class Video Playlist

[Use the arrows in the sides of the screen to scroll through the class videos.]

Material for Lecture 18 on Wednesday 3/11/09

Today:

• Review of Material since Midterm

Next Time:

• There is no next time.

Video:

Topics for Final

We covered the following topics in the course:

1. Assumption required for estimates to be BLUE

2. Hypothesis testing:

a. t- tests (both one-sided and two-sided)
b. Joint hypotheses (F-Tests, Chi-square tests, etc.)

i.  Exclusion restrictions
ii. Linear combinations of parameters

3. Heteroskedasticity

a. What is heteroskedasticity?
b. How heteroskedasticity occur?
c. The consequences of estimating a heteroskedastic model with OLS
d. Tests

i.   LaGrange Multiplier Tests (Models  1, 2, and 3)

Model 1:
Model 2:
Model 3:

ii.  Goldfeld-Quandt test
iii. White's test

e. Corrections/Estimation procedures

i.   Multiplicative:
ii.  Feasible GLS

Model 1:
Model 2:
Model 3:

iii. White’s correction

8. Autocorrelation

a. What is it and why might it occur?
b. Consequences of ignoring serial correlation and estimating with OLS

i.   Model including a lagged dependent variable
ii.  Model with serially correlated errors
iii. Model with both a lagged dependent variable and serial correlated errors.

c. Tests for serial correlation

i.   The Durbin-Watson test.
ii.  Durbin's h-test.
iii. The Breusch-Godfrey test for higher order serial correlation.

d. Corrections

i.  Non-linear estimation
ii. The CORC procedure

9. Testing for ARCH errors

Material after Midterm

10. Stochastic Regressors and Measurement Errors

a. Assessing the bias and consistency of an estimator
b. Errors in variables

i. Consequences of estimating with OLS (differences in mismeasurement. of  the dependent variable and the independent variables).
ii. Application of errors in variables: Friedman's Permanent Income Hypothesis.

c. Instrumental variable estimation

i. What is an instrument.
ii. How is IV performed?
iii. Show how IV estimation can solve the problem of correlation of the right-hand side variables with the error term.

11. Simultaneous equation models

a. Structural equations (behavioral, identities, equilibrium conditions, technical equations) and reduced form equations. Endogenous, exogenous, and predetermined variables.
b. Consequences of ignoring simultaneity, i.e. demonstrate simultaneity bias.
c. Underidentified models, exactly identified models, and overidentified models

d. Estimation by 2SLS

12. Multicollinearity

a. What is multicollinearity and how does it affect OLS estimates and standard errors?
b. Detection of multicollinearity
c. What to do for perfect and imperfect multicollinearity.

13. Specification tests

a. LM test for adding a variable to a model (with and without endogeneity)

14. Qualitative and limited dependent variables

a. Linear probability model

i. description of model, problems, and estimation

b. Probit model

i. description of model and estimation

c. Logit model

i. description of model, attractive properties, and estimation

d. Limited dependent variables

i. description of the model when the dependent variable is limited, problems with OLS, and estimation

15. Maximum likelihood

a. Brief description of what maximum likelihood estimation does.
b. properties of maximum likelihood estimators.

Material for Lecture 17 on Monday 3/9/09

Today:

• Finish Chapter 10 - Limited and Qualitative Dependent Variables
• Maximum Likelihood Estimation

Next Time:

• Review material since midterm

Video:

Homework 8

1. Consider the following simple Keynesian macroeconomic model of the U.S. economy. [Macro data set]

Y_t = CO_t + I_t + G_t + NX_t

COt = β₀ + β₁YD_t + β₂CO_t-1 + ε_1t

YD_t = Y_t – T_t

I_t = β₃ + β₄Y_t + β₅r_t-1 + ε_2t

r_t = β₆ + β₇Y_t + β₈M_t + ε_3t

where:

Y_t = gross domestic product (GDP) in year t
CO_t = total personal consumption in year t
I_t = total gross private domestic investment in year t
G_t = government purchases of goods and services in year t
NX_t = net exports of goods and services (exports - imports) in year t
T_t = taxes in year t
r_t = the interest rate in year t
M_t = the money supply in year t
YD_t = disposable income in year t

Endogenous variables: Y_t, YD_t, CO_t, I_t, r_t,
Exogenous and predetermined variables: G_t, NX_t, T_t, M_t, CO_t-1, and r_t-1

(a) Using OLS, estimate equations for CO_t and I_t.
(b) Using 2SLS, estimate equations for CO_t and I_t.

2. Finish your project and turn it in on Thursday, March 12 in lab.

Project Write-Up

Here's a few general guidelines to help with the write-up of your empirical project. Let me stress once again that your main goal for the project is to show that you understand how to use the tools and techniques we learned in class:

1. Introduction

Introduce the problem and discuss the question you are trying to answer with your empirical project.

2. Theory and Hypotheses

Discuss the theory underlying your model and state the hypotheses you are going to test. You should also state the significance levels you will use in your tests.

3. Empirical Model and Data

Present the empirical model you are using to test your hypotheses. This is where specification issues should be addressed. For example, did you log your data? Did you include squared terms or interactions? Are there any important omitted variables? If so, what are the consequences? Did you use tests to see if variables you weren’t sure about belong in the model? You should also discuss the data and data sources in this section.

4. Violations of Assumptions

At this point, you have the basic empirical model specified and you have discussed specification issues. You should now discuss potential violations of the Guass-Markov conditions. The goal is to test for heteroskedasticity or serial correlation, and then either correct your model for the problem if it exists, or describe how you would have corrected the model had you found a problem. There are direct tests for heteroskedasticity and autocorrelation, but you should also discuss any other notable violations of the assumptions that may be present in your model and how those will be handled or accounted for. For example, are measurement errors a problem? Do you need to use instrumental variables to solve any endogeneity problems?

5. Results

Now that you have described the specification of the model, and described how you checked and corrected for any problems that exist, you are now ready to present estimates of your final model. After presenting the final estimates, you should discuss the overall fit of the model, and interpret the coefficients. What do the coefficients tell you? This is also the section where you should present the test results for the hypotheses you are examining, and then discuss the results.

6. Conclusion

What did you learn? Did the data support your hypotheses? How could you improve the model? What could you do in a follow-up study to learn more about this topic?

Material for Lecture 16 on Wednesday 3/4/09

Today:

• Continue Chapter 10 - Limited and Qualitative Dependent Variables

Next Time:

• Continue Chapter 10 - Limited and Qualitative Dependent Variables

Video:

Material for Lecture 15 on Monday 3/2/09

Today:

• Begin Chapter 10 - Limited and Qualitative Dependent Variables

Next Time:

• Continue Chapter 10 - Limited and Qualitative Dependent Variables

Video:

Homework 7

[Due Thursday March 5 in lab.]

1. Problem 9.3 on page 276 of the text.

2. For the model

Q_t = a₀ + a₁P_t + a₂Y_t + a₃X_t + a₄Z_t + u_t
P_t = b₀ + b₁Q_t + b₂Y_t + b₃W_t + v_t
Y_t = c₀ + c₁P_t + c₂W_t + w_t

Determine whether each equation is under, exactly, or over identified.Assume that Q, P, and Y are endogenous, and that the constant, X, Z, and W are exogenous.

3. Answer the following questions about your project:

(i) Do you expect any measurement problems, i.e. do you expect to have errors in variables problems? If so, what effect will that have on your estimates and test statistics (if you don't think this will be a problem, say that and explain why, and then say, but if I did have this problem it would cause the following difficulties and then describe the effect it would have on the estimates and test statistics). How can the problem be fixed?

(ii) Are there any important omitted variables? If so, what effect would the omitted variables have on the estimates and test statistics? (And again, even if you think you have every important variable, show that you understand this issue by explaining what types of problems it causes).

(iii) Do you expect problems with endogeneity bias (endogenous varaibles on the right-hand side of the equation that are correlated with the error term)?  Think hard about this one, and if you do have this problem, what is the solution?

Material for Lecture 14 on Wednesday 2/25/09

Today:

• Continue Chapter 9 - Simultaneous Equations Estimation

Next Time:

• Finish Chapter 9 - Simultaneous Equations Estimation, Begin Chapter 10

Video:

Material for Lecture 13 on Monday 2/23/09

Today:

• Continue Chapter 9 - Simultaneous Equations Estimation

Next Time:

• Continue Chapter 9 - Simultaneous Equations Estimation

Video:

Homework 6

1. Problem 8.5 on page 253, part 1 only.

2. Consider the following simple Keynesian macroeconomic model of the U.S. economy.

Y_t = C_t + I_t + G_t + NX_t

C_t = β₀ + β₁YD_t + β₂C_t-1 + ε_1t

YD_t = Y_t – T_t

I_t = β₃ + β₄Y_t + β₅r_t-1 + ε_2t

r_t = β₆ + β₇Y_t + β₈M_t + ε_3t

where:

Y_t = gross domestic product (GDP) in year t
C_t = total personal consumption in year t
I_t = total gross private domestic investment in year t
G_t = government purchases of goods and services in year t
NX_t = net exports of goods and services (exports - imports) in year t
T_t = taxes in year t
r_t = the interest rate in year t
M_t = the money supply in year t
YD_t = disposable income in year t

The endogenous variables are Y_t, C_t, I_t, YD_t, and r_t. The exogenous and predetermined variables are G_t, NX_t, C_t-1, T_t, r_t-1, and M_t.  Find the reduced form equations for this model.

3. (a) For your project, what econometric model do you plan to estimate and what hypothesis or hypotheses do you plan to test? (b) Depending upon whether your data are time-series or cross-sectional, test the model for autocorrelation or heteroskedasticity. (c) If you find a problem with either, explain explicitly how you plan to correct for it. If the tests do not indicate a problem, explain how you would have corrected for the problem had the test come out the other way (that is, no matter how the test comes out, explain how to correct for the problem of heteroskedasticity or autocorrelation as appropriate for your model. You don't have to actually do the correction for this homework (though if it was present, you would do the correction for the project), just explain how to do it.).

Material for Lecture 12 on Wednesday 2/18/09

Today:

• Chapter 9 - Simultaneous Equations Estimation

Next Time:

• Continue Chapter 9 - Simultaneous Equations Estimation

Video:

Material for Lecture 11 on Monday 2/16/09

Today:

• Chapter 8 - Stochastic Regressors and Measurement Errors

Next Time:

• Chapter 9 - Simultaneous Equations Estimation

Video:

Homework #5

1. Complete steps 1 through 3 of the Empirical Project Outline (as discussed in class).

2. Problem 8.3 on page 253.

3. What are the three requirements for a good instrumental variable? [We'll cover this on Monday.]

---

[Note: The *next* homework will ask: (a) For your project, what econometric model do you plan to estimate and what hypothesis or hypotheses do you plan to test? (b) Depending upon whether your data are time-series or cross-sectional, test the model for autocorrelation or heteroskedasticity. (c) If you find a problem with either, explain explicitly how you plan to correct for it. If the tests do not indicate a problem, explain how you would have corrected for the problem had the test come out the other way (that is, no matter how the test comes out, explain how to correct for the problem of heteroskedasticity or autocorrelation as appropriate for your model).]

Midterm

Midterm Exam and Solution.

Material for Lecture 10 on Wednesday 2/4/09

Today:

• Chapter 8 - Stochastic Regressors and Measurement Errors

Next Time:

• Continue Chapter 8

Video:

Topics for Midterm

1. Assumption required for estimates to be BLUE

2. Hypothesis testing:

a. t- tests (both one-sided and two-sided)
b. Joint hypotheses (F-Tests, Chi-square tests, etc.)

i.  Exclusion restrictions
ii. Linear combinations of parameters

3. Heteroskedasticity

a. What is heteroskedasticity?
b. How heteroskedasticity occur?
c. The consequences of estimating a heteroskedastic model with OLS
d. Tests

i.   LaGrange Multiplier Tests (Models  1, 2, and 3)

Model 1:
Model 2:
Model 3:

ii.  Goldfeld-Quandt test
iii. White's test

e. Corrections/Estimation procedures

i.   Multiplicative:
ii.  Feasible GLS

Model 1:
Model 2:
Model 3:

iii. White’s correction

8. Autocorrelation

a. What is it and why might it occur?
b. Consequences of ignoring serial correlation and estimating with OLS

i.   Model including a lagged dependent variable
ii.  Model with serially correlated errors
iii. Model with both a lagged dependent variable and serial correlated errors.

c. Tests for serial correlation

i.   The Durbin-Watson test.
ii.  Durbin's h-test.
iii. The Breusch-Godfrey test for higher order serial correlation.

d. Corrections

i.  Non-linear estimation
ii. The CORC procedure

9. Testing for ARCH errors

The Cochrane-Orcutt Procedure

The Cochrane-Orcutt procedure:

One note: In step 5 when it says to use the estimated betas obtained in step 4 in equation  (9.5),  this means to go back to the origanal equation (9.5) and find u_t = Y_t - b₁ - b₂X_2t  - ... - b_kX_kt where the b's are the estimated betas using the transformed ("starred") variables in step 4. However, be careful about obtaining the value of b₁. Note from above in equation (9.9) that you have to divide the estimate of the constant from the regression involving the "starred" values by 1-ρ in order to obtain b₁.

Material for Lecture 9 on Wednesday 2/4/09

Today:

• Chapter 12 - Finished Autocorrelation
• Outline and Review of Material for Exam

Next Time:

• Midterm

Video:

Empirical Project Outline

Here is a brief outline of the project. We will talk more about this in class:

1. Statement of theory and hypothesis

• What is the hypothesis or hypotheses that you are testing? Be explicit.
• What does theory say about each hypothesis you are interested in testing, i.e. what are the theoretical predictions?

2. Specification of the econometric model

• Specify the econometric model you will estimate. What variables will be in the model? Will you take logs, add squares of variables, or do any other transformations of the data?
• What sign do you expect each coefficient to have, and what is the interpretation of the coefficients?
• Do you expect to have any trouble with the error term such as serial correlation or heteroskedasticity?

3. Obtain data

• What would an ideal data set look like? What data are actually available? Where will you get the data. Be specific about data sources.

4. Estimation of the econometric model and diagnostic tests

• What estimation technique will you use?
• What problems will you test for? If you detect problems, how will you correct for them?

5. Test hypotheses

• What tests will you conduct and what significance level will you use to evaluate the outcome?

6. Forecasting or prediction

• How can you use the model you have estimated to make forecasts or predictions?

It will take longer than you think to do the estimation stage, so give yourself plenty of time. When the project is finished, it may or may not turn out the way you hoped. That's okay, you will not be graded on how clever you are at finding an interesting hypothesis to investigate, or on whether you find out anything particularly noteworthy when you are done, though you might. The goal is for you to illustrate that you know how to use the tools and techniques that we learn in class, and that is the basis for the evaluation of the projects.

"Cereal Correlation "

This is from The Monkey Cage:

56% of women who consumed the most calories before conception gave birth to boys, compared with 45% of those who consumed the least. Of 132 individual foods tracked, breakfast cereal was the most significantly linked with baby boys.

That’s from a study by researchers at Exeter and Oxford, as per Melinda Beck’s write-up in the Wall Street Journal.

This made me wonder. After all, my brothers and I turned out to be, well, boys, and my mother never ever ate breakfast cereal. However, as a social scientist I recognize that correlational results admit of exceptions.

They also, as Beck notes, occasion doubt. One of the first things one is supposed to learn about “statistical significance” is that some results that appear to be real, aren’t. If you’re operating at the .05 significance level, then in the long run somewhere around 5% of the relationships that you accept as non-random should really be random. Those are “Type 1” errors — or are they “Type 2” errors? I could never keep those straight. (Andrew, though not not a frequentist, presumably can straighten me out here.) Anyway, these breakfast cereal results apparently have produced a minor kerfuffle among epidemiologists and statisticians, which you can read about in the Beck article. If nothing else, this episode provides a nice example for those who are teaching intro methods courses, and it also gives “Monkey Cage” readers an opportunity to admire the excellent pun I devised for the headline of this item. (Please hold your applause.)

Homework #4

Economics 421/521
Winter 2009
Homework #4
Due in lab on Thursday, Feb. 5

1. Perform a Durbin-Watson test at the 5% level of significance for positive first-order autocorrelation using the following regression output (standard errors in parentheses):

Y_t = 2.0 + 3.7*X_1t - 4.4*X_2t,    T = 42
       (.7)   (1.1)          (2.8)           DW = 1.22

2. Recall the model from homework 1:

Given data on M2, real GDP, and the T-bill rate, estimate the following regression...:

M_t = β₀ + β₁RGDP_t + β₂Tbill_t + e_t

Don't be surprised if the fit is very good - we'll explain why that may be misleading later in the course.

Does model suffer from serial correlation? Use a Durbin-Watson test to answer the question. Is the fit as good as the R² and t-statistics indicate?

3. Regress the change in the log of real consumption (C) on the change in the log of real disposable income (DI) and test for serial correlation using a Durbin-Watson test. The data are here (the data are quarterly, and span the time period 1947:Q1 - 2007:Q3).

4. Explain why the Durbin Watson statistic is always between 0 and 4. Also explain why the Durbin-Watson statistic is between 0 and 2 when there is positive serial correlation, between 2 and 4 when there is negative serial correlation, and equal to 2 when there is no correlation at all.

5. Continuing with the model we used in problem 2, test for the presence of fourth order serial correlation.

6. Continuing with the model we used in problem 3, use the AR(1) procedure in EViews to correct the model for the presence of first-order serial correlation.

Material for Lecture 7 on Wednesday 1/28/09

Today:

• Chapter 12 - Autocorrelation

Next Time:

• Continue Chapter 12 - Autocorrelation

Video:

Material for Lecture 6 on Monday 1/26/09

Today:

• Chapter 12 - Autocorrelation

Next Time:

• Continue Chapter 12 - Autocorrelation

Video:

Homework 3

[Note: The assignment will be discussed in lab on 1/22, and will be due in lab on 1/29.]

Economics 421/521
Winter 2009
Homework #3

1. Using the first model of heteroskedasticity, i.e. that resid² = α₀ + α₁*years + α₂*years², correct the salary model in problem 3 from Homework 2 for heteroskedasticity and reestimate.

2. Problem 7.2 in the text.

3. Test the salary model in problem 3 from Homework 2 for heteroskedasticty using White's test. Correct the standard errors using White's correction. How do the coefficients and corrected standard errors compare to those obtained in problem 3 of Homework 2?

4. What are the consequences of estimating an autoregressive model using OLS?

[Note: pdf of problems 7.1 and 7.2, problem 7.1 was on the last homework.]

Material for Lecture 5 on Wednesday 1/21/09

Today:

• Continue Chapter 7 - Heteroskedasticity

Next Time:

• Chapter 12 - Autocorrelation

Video:

LM Tests for Heteroskedasticity

Here is an outline of the LM tests for Heteroskedasticity:

Homework 2

[Note: The assignment will be discussed in lab this week, and will be due in lab next week.]

Economics 421/521
Winter 2009
Homework #2

1. Using the EAEF data set, regress LGEARN on S, EXP, and ASVABC. Use F-tests to determine whether the coefficients on S and EXP are (a) jointly significant, and (b) equal. [Parts (a) and (b) are two separate tests.]

Note: Here are the variable definitions (see pages. 443-444 in Appendix B of the text):

• EARNINGS = current hourly earnings in $ reported in 2002 interview.
• S = Years of schooling (highest grade completed as of 2002).
• EXP = Total out-of-school work experience (years) as of the 2002 interview.
• ASVABC = Scaled standardized test score.

2. Problem 7.1 in the text.

3. Using this data set, repeat the example from class for the first of the three cases we discussed, i.e. first regress the log of salary on a constant and the two variables proxying for experience, years and years²:

     log(salary) = β₀ + β₁*years + β₂*years² + u_t

Then, form the estimated residual squared (resid²) and perform the LM test for heteroskedasticity (note: resid is the estimated value of u_t).

[Note: pdf of problems 7.1 and 7.2, problem 7.2 will be on the next homework.]

Material for Lecture 4 on Wednesday 1/14/09

Today:

• Continue Chapter 7 - Heteroskedasticity

Next Time:

• Continue Chapter 7 - Heteroskedasticity

Video:

Material for Lecture 3 on Monday 1/12/09

Today:

• Continue Chapter 7 - Heteroskedasticity

Next Time:

• Continue Chapter 7 - Heteroskedasticity

Video:

Homework 1

[Note: The assignment will be discussed in lab this week, and will be due in lab next week.]

Economics 421/521
Winter 2009
Homework #1

Part I. Hypothesis Testing

1. Suppose that you estimate a model of house prices to determine the impact of having beach frontage on the value of a house.  After researching the problem, you decide to use the size of the lot instead of the size of the house as your explanatory variable for a number of theoretical and data availability reasons.  The results (standard errors in parentheses) are:

PRICEi = 40 + 35.0 LOTi – 2.0 AGEi + 10.0 BEDi – 4.0 FIREi + 100 BEACHi
        (29) (5.0)       (1.1)      (10.0)      (3.0)       (9.0)

where n = 30, R2 = .63, and PRICE_i = the price of the i^th house (in thousands of dollars), LOT_i = the size of the lot of the i^th house (in thousands of square feet), AGE_i = the age of the i^th house in years, BED_i = the number of bedrooms in the i^th house, FIRE_i = a dummy variable for a fireplace (1 = yes for the ith house), and BEACH_i = a dummy for having beach frontage (1 = yes for the ith house).

a) You expect the variables LOT, BED, and BEACH to have positive coefficients.  Test this hypothesis at the 5 percent level.

b) You expect AGE to have a negative coefficient.  Test this hypothesis at the 10 percent level.

c) At first you expect FIRE to have a positive coefficient, but one of your friends says that fireplaces are messy and are a pain to keep clean, so you are not sure.  Run a two-sided t-test around zero to test the two-sided hypothesis at the 5 percent level.

2. Consider the following regression:

log(Qci) = 921.6 – 1.3 log(Pci) + 0.7 log(Pai) + 11.4 log(Inci) 
           (121)  (0.3)          (0.05)          (2.8)

where n = 30, R2 = 0.82, and  where Qc_i = the total sales of CAMRY in the ith city in 2003, Pc_i = the price of a CAMRY in the i^th city in 2003 (in thousands), Pa_i = the price of an ACCORD in the i^th city in 2003 (in thousands), and Inc_i = the average income in the i^th city, the year of 2003 (in thousands).  The numbers in the parentheses are standard errors.

a) How is the constant term interpreted?

b) How would you interpret the coefficient on log(Pc_i).  Be explicit and explain, in terms of economic theory, the importance of its magnitude.

c) Get t-values for the coefficients in the regression.  Are all of our coefficients statistically significant at the 5% level of significance?  How about at the 1% level of significance?

d) Interpret R². Can we have a negative R²?

Part II. Short Answer

1. State the Gauss-Markov Theorem and explain the term BLUE.

Part III. Estimation

1. Given data on M2, real GDP, and the T-bill rate, estimate the following regression and test whether the coefficients differ from zero. Do the coefficients have the expected signs?:

M_t = β₀ + β₁RGDP_t + β₂Tbill_t + e_t

Don't be surprised if the fit is very good.  We'll explain why the good fit is misleading in this model later in the course.

Material for Lecture 2 on Wednesday 1/7/09

Today:

• Review of hypothesis testing
• Chapter 7 - Heteroskedasticity

Next Time:

• Continue Chapter 7 - Heteroskedasticity

Video:

Material for Lecture 1 on Monday 1/5/09

Today:

• Review of regression models
• Assumptions required for estimates to be BLUE ( pgs. 68-71 and 127-128)
• Guass-Markov Theorem (pg. 90-93)

Next Time:

• Hypothesis Tests
• Heteroskedasticity (Chapter 7)

Video